Abstract

A spectrally sparse signal of order r is a mixture of r damped or undamped complex sinusoids. In this talk, we consider the problem of reconstructing spectrally sparse signals from a random subset of n regular time domain samples, which can be reformulated as a low rank Hankel matrix completion problem. We introduce a fast iterative hard thresholding (FIHT) algorithm for efficient reconstruction of spectrally sparse signals via low rank Hankel matrix completion. Theoretical recovery guarantees have been established for FIHT, showing that  number of samples are sufficient for exact recovery with high probability. Empirical performance comparisons establish significant computational advantages for FIHT. In particular, numerical simulations on 3D arrays demonstrate the capability of FIHT on handling large and high-dimensional real data.